19 Ps 36.1 In whose heart is the oracle speaking?
The literal Hebrew is: An oracle (H5002) within (H7130) my (H589, personal pronoun me, mine, myself) heart (H3820).
These translations represent the oracle as speaking within the psalmist’s heart:
HCSB: an oracle within my heart
NIV84: an oracle is within my heart
YLT: is affirming within my heart
NKJV: an oracle within my heart
1890 Darby: uttereth within my heart
Geneva: even in mine heart
These translations represent the oracle as speaking within the wicked person’s heart:
ESV: transgression speaks to the wicked deep in his heart
NASB95: transgression speaks to the ungodly within his heart
AMP: transgression (like an oracle) speaks to the wicked deep in his heart
Given that “my” translates ʾ anî, a personal possessive pronoun, I judge that the first set of English translations is the correct interpretation.